GPT-4 Explains — “From Unitary Models to Game Theory: The Evolution of Economic Theories of Marriage and Their Impact on Understanding Domestic Violence”

Tracing the Theoretical Lineage of the Outside Option in Modern Empirical Work on Family Violence by Cunningham (r) and GPT-4 (r)

Off and on throughout Saturday, sometimes while I was watching television with my girls or sitting on the porch on a nice day, I prompted GPT-4 to write this essay. I’d read an article in which it was rumored Buzzfeed had laid off its news group and was now having AI generate articles. The idea that content mills would move towards generative AI in the extreme seems to be very likely given how easy it is to “paint articles” using GPT-4 as the brush. So I thought it would be good to try again in this series, and I chose this as my topic: the evolution of theoretical models of marriage in economics and their role in empirical work on domestic violence.

I know this literature but I’d noticed, as I’m sometimes inclined to when I find myself exiting an area, I’d begun to feel like I couldn’t remember everything by heart. Essays like this I have to go back and remind myself of things by rereading, as well as usually developing some new idea, but here it was more I just wanted to lazily get the idea together and see if I could paint the essay from memory. Painting is the metaphor I tend to use when I think of using generative AI to produce content. It’s not writing; it’s something else. But I still hold the brush. As before, no edits and prompts are at the end.

How satisfied am I with this essay? It feels in the end topical and speculative in parts, plus it seems to get elements wrong from time to time. Where I couldn’t remember details about models and asked GPT-4 to help me is where I am less confident. And getting the entire essay to hang together top to bottom was not how I like to write. But it worked enough for this.

I will say though — GPT-4 without human editing is a challenge because you’ve got to ultimately rewrite sections using the brush approach. I reread the essay, and I now realize how much of the interesting work in draft form we made got dropped in the final version. I think this was where it just merged the two household models as there’s no mention of Pareto efficiency. That’s buried in the drafts of the chat box. Probably what I would do if I wasn’t on my phone is I would’ve copied and pasted sections I liked and then went on rather than constantly asking it to rewrite sections. I think the prompt or “rewrite this” is telling GPT-4 to make it more succinct which inevitably leads it to edit out details I wanted in.

Introduction

In a recent presentation by Emily Nix from the University of Southern California, a unique approach to understanding domestic violence was presented. Using Scandinavian linked registry data, Nix and her team were able to uncover a striking pattern: when a woman entered a cohabiting relationship with a man who would later turn out to be abusive, her labor market outcomes dramatically declined soon after cohabitation began. The researchers posited that the abusive partner was systematically undermining the woman's outside options, effectively trapping her in an abusive relationship.

To the uninitiated, this scenario raises several questions. Why are economists studying domestic violence, a topic seemingly more suited to the realms of sociology, psychology, or law? And what exactly are these "outside options" that the researchers refer to?

The aim of this essay is to address these questions by delving into the theoretical underpinnings of economic thought as it pertains to marriage, relationships, and domestic violence. We will trace the evolution of economic marriage models from their roots in the work of Becker and game theorists like Gale and Shapley, through to modern applications in empirical research on domestic violence.

The goal is to illuminate how these models have shaped our understanding of the dynamics within households and the role of outside options. In doing so, we hope to provide readers with a clearer understanding of the fundamental ideas that underpin much of the current empirical work on domestic violence within the family. This journey through the theoretical landscape is crucial in enabling us to appreciate the complex and often subtle factors that underpin the reality of domestic violence in our society today.

Part 2: Tracing the Theoretical Evolution

The quest to understand the dynamics of marriage first found footing in game theory, with the pioneering work of David Gale and Lloyd Shapley. Their 1962 model explored two-sided marriage markets, introducing the 'deferred acceptance algorithm', a process that has since become a cornerstone in the economic understanding of marriage markets. Gale and Shapley's model allowed individuals to rank potential partners according to their preferences, leading to proposals, acceptances, rejections, and an eventual equilibrium that ensured stability – where no two individuals would prefer being with each other over their current partners.

However, the model's scope was limited to the formation of pairings and did not extend to the consumption or distribution of outcomes within these formed pairs. It offered no insight into the economic transactions occurring within the confines of a household, a gap that was later addressed by economist Gary Becker.

Becker's 1973 theoretical framework blended elements of consumer and producer theory into the analysis of marriage. He introduced a new perspective on marriage, seeing it as a decision rooted in utility maximization under budget constraints. Becker's utility function was described as:

U = U(Z, C, L)

Here, Z represents commodities produced within the household, C denotes commodities purchased from the market, and L signifies leisure. Households were assumed to maximize this utility function subject to the time constraint T = L + H, where T stands for the total available time, L represents leisure, and H is the time spent on work.

The budget constraint, under Becker's model, was given by:

I = wH + Y

where I represents the total income, w is the wage rate, H is hours worked, and Y is non-labor income.

Becker's model offered a significant insight: marriage, as a decision, led to increased efficiency in resource allocation owing to the division of labor. However, the model was built on the assumption of a harmonious household, where a single entity, typically the household head, made decisions to maximize total utility. Becker did attempt to account for potential discord within the household in his later work by introducing the "rotten kid theorem", a mechanism that relied on monetary transfers to encourage cooperation. This method, while innovative, was eventually replaced with a more generalized transferable utility concept in the broader literature, as it better captured the complex dynamics of households where resources were often allocated based on factors beyond monetary considerations, such as love and affection.

Despite these attempts to incorporate intra-household dynamics, Becker's model did not explicitly model the role of outside options, a crucial element in understanding household bargaining and its implications on domestic violence. This aspect was later addressed by the emergence of a new theoretical framework in the 1980s, heavily influenced by the seminal work of John Nash and Ariel Rubinstein. The stage was thus set for the introduction of a fresh perspective on household dynamics, bringing into focus the concept of bargaining within households and the role of outside options.

Part 3: Introduction of Bargaining in Game Theory

Game theory, a field pivotal in understanding strategic behavior, made significant strides in the 1950s and 60s. The work of John Nash, who introduced the Nash bargaining solution in his 1950 dissertation,

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was instrumental in shaping the course of this discipline. Nash proposed that two parties involved in negotiation could achieve a mutually satisfactory outcome by carefully strategizing their moves. Although Nash's work was primarily theoretical, it opened doors to a new way of viewing negotiation and bargaining processes.

The 1980s saw the rise of Ariel Rubinstein, who significantly extended the reach of bargaining theory. He expanded Nash's cooperative bargaining model to non-cooperative scenarios, providing a deep insight into how bargaining outcomes could be influenced by factors like the order of moves, available outside options, and patience or impatience of the negotiating parties.

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The Nash bargaining solution was characterized by two essential elements: the threat point (or disagreement point) and the bargaining set. The threat point represented the minimum outcome a player would accept, while the bargaining set comprised the range of mutually acceptable outcomes.

Applying this to the context of marriage, the Nash bargaining solution had profound implications. It suggested that resource allocation within a marriage wasn't solely dependent on the spouses' preferences. Instead, it was also shaped by their relative bargaining power, which in turn could be influenced by various factors such as income, education, and prevailing social norms.

The advent of these game-theoretic models marked a departure from the unitary model of the household proposed by Becker. They introduced a more nuanced perspective on household decision-making, which was instrumental in setting the stage for the groundbreaking household models that emerged in the 1980s.

One may speculate why the transition from the unitary model to bargaining models happened in the early 1980s. It seems that the game-theoretic approach to bargaining, initially applied to labor and business negotiations, naturally found its way into household economics. The time was ripe, as the 1970s and 80s saw an increasing interest in the economics of the family. Furthermore, it's interesting to note that Robert Pollak, who would later extend the household bargaining model with Shelly Lundberg, served as the editor of the International Economic Review (IER) that published seminal papers on household bargaining models in 1980 and 1981. This may have contributed to the shift towards a game theoretic understanding of family economics.

Part 4: Introduction of Household Bargaining Models

As we delve deeper into the early 1980s, we encounter two landmark papers that introduced new household models, challenging the unitary model's simplistic assumptions. These papers were authored by Marilyn Manser and Murray Brown, and Marjorie McElroy and Mary Jean Horney.

Marilyn Manser was a researcher at the Bureau of Labor Statistics, and Murray Brown was a professor of Economics at the University of British Columbia at the time. Their collaboration yielded a pioneering paper titled "Marriage and Household Decision-Making: A Bargaining Analysis," published in the International Economic Review in 1980.

Marjorie McElroy, a professor at Duke University, and Mary Jean Horney, a professor at the University of North Carolina at Greensboro, penned their groundbreaking paper "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand" in the same year.

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Manser and Brown began their paper with a critique of the unitary model. They contended that the unitary model's assumption of a single, unified household decision-maker was too simplistic. In their view, a more realistic depiction of household decision-making would involve bargaining between spouses, with each spouse striving to maximize their utility.

Their model was rooted in Nash's bargaining solution, where each spouse's utility was dependent on their consumption and the family's public goods. They refrained from explicitly referring to "power" but suggested that a spouse's bargaining position would be influenced by their income, social norms, and outside options.

The outside option or "threat point" in their model was the utility level each spouse would achieve if the bargaining process failed, i.e., if they were to separate or divorce. The threat point was essential in shaping the allocation of resources within the household. If one spouse's outside option improved (for instance, through an increase in their personal income or changes in divorce laws), their bargaining power would increase, leading to a more favorable allocation of resources for them.

In the next section, we will delve into the McElroy and Horney model, which, while similar to Manser and Brown's model, introduced some unique elements.

Part 5: Further Refinements in Household Bargaining Models - McElroy and Horney

Marjorie McElroy and Mary Jean Horney, in their 1981 paper "Nash-Bargained Household Decisions: Toward a Generalization of the Theory of Demand", introduced another bargaining model that was a significant step forward in the field. Although their model shared many similarities with Manser and Brown's work, it had some crucial differences that set it apart.

Their model's starting point was similar to that of Manser and Brown: a critique of the unitary model and its oversimplification of household decision-making processes. They proposed a model that recognized the potential for conflict and negotiation within households, incorporating the concept of Nash bargaining into their framework.

The utility functions in their model were structured similarly to those in Manser and Brown's model, but they introduced an outside option or "threat point" explicitly tied to a spouse's well-being in case of non-cooperation or divorce. Each spouse's utility was, therefore, a function of their private consumption, family public goods, and their outside option.

The outside option played a crucial role in the negotiation process. It represented each spouse's potential welfare level if the marriage were to dissolve, thus influencing their bargaining power within the marriage. A higher outside option, achieved through factors like higher personal income or favorable divorce laws, would result in a stronger bargaining position and a more favorable allocation of resources within the household.

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At this point, by the end of 1981, the landscape of economic models of the household had changed significantly. The unitary model had been challenged, and bargaining models that allowed for individual utilities and outside options had been introduced. These new models were more attuned to the complexities and nuances of household decision-making, reflecting the different preferences, incomes, and bargaining powers of spouses. In the next section, we'll explore how these theoretical developments were incorporated into empirical research.

Part 6: Empirical Household Models and the Emergence of New Data

The 1970s and 1980s saw economists increasingly focused on empirical studies of marriage, divorce, and household behavior. Early work in this realm was primarily trend-focused, akin to demographic studies. One pioneer in this field was Jacob Viner, whose work on the role of economics in shaping family decisions laid the groundwork for future empirical studies.

However, it was the introduction of bargaining models that truly spurred empirical research into household behavior. The models proposed by Manser and Brown and McElroy and Horney provided a new lens through which economists could study households, offering testable predictions that could be explored with real-world data.

An early and influential empirical study in this line of work was by Shelly Lundberg, Robert A. Pollak, and Terence J. Wales. Their 1997 paper "Do Husbands and Wives Pool Their Resources? Evidence from the United Kingdom Child Benefit" was a significant contribution to the empirical literature on household bargaining models.

They used an intriguing natural experiment in the UK where the government had shifted the recipient of child benefits from husbands to wives. Under Becker's unitary model, this shift shouldn't have affected household consumption as the total income remained unchanged. However, under the bargaining models, this change effectively increased wives' non-labor income and thus their bargaining power.

Lundberg, Pollak, and Wales found that, despite the total household income remaining constant, the consumption of child and female-specific goods increased following the policy change, while male-specific goods like alcohol and tobacco saw a decrease. This supported the predictions of the bargaining models and indicated that shifts in bargaining power within households could significantly impact household consumption patterns.

This study set the stage for a surge of empirical work using household bargaining models, much of which, as we will see in the next section, has focused on the implications of bargaining power dynamics for domestic violence.

Part 7: From Bargaining Power to Domestic Violence: The Work of Stevenson and Wolfers

The growing interest in the economics of the household and the increasing availability of sophisticated empirical techniques led to some unexpected but important areas of study. One such area, which may initially seem surprising in an economics context, is the study of domestic violence.

Betsey Stevenson and Justin Wolfers made notable contributions to this field by linking economic concepts such as bargaining power, property rights, and the Coase theorem to the incidence of domestic violence. Their work emphasized the influence of unilateral divorce laws on the distribution of power within marriages and, in turn, the occurrence of domestic violence.

The Coase theorem, a fundamental principle in economics, posits that if transaction costs are low, the allocation of property rights doesn't matter as individuals can freely negotiate to achieve a socially optimal outcome. However, if transaction costs are high, the allocation of property rights becomes crucial.

Stevenson and Wolfers applied this reasoning to marriage and divorce. They argued that prior to unilateral divorce laws, the spouse wanting to keep the marriage intact had the power. However, under unilateral divorce laws, the spouse wanting to exit the marriage gained power. They suggested that this shift in power had a significant impact on the incidence of domestic violence.

Using a difference-in-differences approach combined with event studies, they examined the effects of changes in divorce laws on suicides and spousal homicides. They found that female suicides fell as a result of the introduction of unilateral divorce laws, providing empirical evidence for their argument.

Their work had a lasting legacy in several ways. It showcased the use of event studies and difference-in-differences methods, provided a basis for the development of bargaining theories of domestic violence, and demonstrated that Becker's unitary model, while valuable, lacked empirical content that could be supplied by game theoretic models.

This trend in empirical work continues, with economists using game theoretical models to study not just domestic violence, but many aspects of household dynamics. It's a testament to the powerful theoretical tools that economists have at their disposal, and a reminder of how these tools can be used to shed light on issues that may initially seem beyond the realm of economics.

Part 8: Conclusion

In conclusion, this essay has charted the historical evolution of economic theories of marriage, tracing their path from unitary models to game-theoretic approaches. A central focus throughout this journey has been the concept of the 'outside option' or 'threat position', an idea rooted in early Nash bargaining models of marriage. This notion has become a cornerstone of economists' empirical contributions to our understanding of domestic violence.

The evolution of these models has been influential, and has provided a rich theoretical framework for examining the dynamics of household decision-making and the distribution of power within households. However, this essay by no means provides an exhaustive exploration of the topic but serves as a simple sketch through the literature from game theory to empiricism.

The theory of outside options in marriage has notably shaped the empirical work in this field and will likely continue to do so, as it has been highly fruitful in enhancing our understanding of domestic violence and the importance of outside options as a deterrent.

Yet, looking ahead, there remains a significant gap in our understanding. While the current models and empirical work have focused on the 'push factors' that influence the decision to leave an abusive relationship, they have largely overlooked the 'pull factors' that may explain the persistence of these relationships, even in the face of available outside options.

The literature on 'high conflict couples' underscores the role of personality disorders in abuse, but these explanations do not fully account for the stability of abusive relationships, which often endure for years beyond the initiation of abuse. Gale and Shapley's work on stable pairing in marriage, based on preferences and the deferred acceptance algorithm, prompts us to think about the issue of sorting into stable abusive relationships.

Why do people stay in abusive relationships when they can leave? What factors pull them together and keep them entwined in such circumstances? These are questions that remain underexplored in economic studies of domestic violence. Future research could benefit from a shift in focus towards understanding these 'pull factors' and the mechanisms behind the sorting into stable partnerships characterized by emotional, psychological, and physical abuse.

The economic analysis of domestic violence has come a long way since the days of unitary models, but there remains much to be discovered. This essay, we hope, serves as both a reflection on the progress made and a call for continued exploration into the complex dynamics of marriage and domestic violence.

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Prompts

Are you familiar with the household bargaining models from 1980 and 1981 by Manser and Brown and McElroy and Horne? They’re Nash bargaining models.

Does the concept of the threat position and outside option appear in these papers or is that later?

Okay, I would like to do a substack on these two models. Do you feel you understand them well enough to help articulate how they differed from the other?

Okay here’s the substack. In this explainer we are going to discuss beckers original unitary utility max theory of marriage and the family. We will discuss the equation the household head maximize and the constraints and solve for demand, as well as how resources are distributed within the family. But then we will discuss the advanced by the Nash models which have become more common.

In part 1, start by discussing the prior work that Becker had done on topics not often considered economics like crime and discrimination. Then lead into family

Rewrite the introduction. Say to this effect that the historical modeling of the family and marriage by economists has gone through stages. Early work by Becker was influential for many years but was gradually replaced by models that reflecting the endogenous sorting into and out of marriage as well as the endogenous distribution of total surplus between (usually) the two marrying individuals. The insight of these models came from old Nash bargaining models which emphasized threat position as a source of negotiation power. Todsy we will discuss two of those papers — McElroy and Horne and Manser and Brown, each published in IER in 1980 and 1981. Now rewritten this. It can be two or more paragraphs. Motivate the importance of the topic — models of the family — first and why economisfs care about it. Emphasize that the family is the social unit where many long lasting outputs are produced such as childcare and education as well as the source of happiness but also mistreatment. Then emphasize we will move between models

Next section covers beckers early models of marriage. Which ones were seminal and the most influential on the marriage and who were the coauthors?

What sort of interaction do we know of between Gale and Shapleys college roommate article in the 1960s which laid out the deferred acceptance algorithm, and Becker’s work on marriage? How much interaction did these two have with each other and what was the others response to their work?

Okay let’s start the section immediately after our opening with the early work in marriage by game theorists and economists starting with gale and shapeley. Note that the paper was influential and is represented extensively in Alvin Roth’s later work in two sided matching. We will call this the game theoretic tradition of marriage which emphasized two sided marriage markets and the deferred acceptance algorithm, As well as the concept of stability. We are leading though into the later game theoretic models but only after moving through bwcker so this discussion of Gale ans shapley is just a starting point

Rewrite this because in the discussion of the two authors and the influence, we want to say that a little about what the deferred acceptance algorithm is. So insert this after “including school choice and organ transplantation” with a new paragraph describing the model, how each person ranks the other side in terms of utility payouts who they’d like to match, one group goesr first and asks for a partner, all other group does is take their most preferred and declines the others. In round two anyone unattached asks their second preferred. This causes some pairings to break down as the person will drop their current partner and accept the new one. This process repeats until the market clears. Whichever side goes first is called the M-optimal or F-optimal stable. The key insight is that it’s stable and who goes first tends to get the better aggregate matches. But this is a formation model. Nothing is done to describe a mechanism by which the output of the pairing gets consumed or by whom. Then when you’re doing, finish as you were going

Next section: Beckers model of marriage 1973. Note that this is not the first time economists studied the family — Jacob Viner has done so, but his work was primarily empirical. Becker’s was unique for tackling the theory of marriage using the tools of consumer and producer theory — competitive markets and utility maximization with budget constraints. Write this up and seamlessly move into this following the Gale and Shapley work.

Rewrite this but don’t repeat parts. It seems like you repeated the parts about prices and marriage markets twice? Also you need to set up the utility function, the budget constraint, in latex, then solve for first order conditions to get demand curves. What is the purpose of Beckers model? What main insights do we learn? We want to focus though on its limitations. There is peace within the bwcker family because the head maximizes utility for the family. But this will be explored again later by the new game theorists

Are you sure that’s the correct utility function?

Okay rewrite this one last time, but has the new equations. Emphasize what we learned from his approach and what maybe was simplified for the sake of gaining those insights.

Perfect. Let’s now briefly give the reader some context about bargaining, a rich literature in game theory, before going into the household models. What is the history of bargaining in game theory? Mention Nashs work mainly and Rubinstein. Walk us topically through the main writers but then let’s zero in on Nash’s models. What are the sources of this work? What are the key EJ elements? What are the publications? What influence did it have?

Let’s now say that with this extreme activity on bargaining taking place in the 1980s as well as Becker’s own work in the 1970s, offer us your own theory as to why the question of a new household model to replace Beckers gets introduced in the early 1980s. Note this small fact not widely known — that Robert Pollack, an economist who would later himself extend the household bargaining model with Shelly Lundberg ten years later, was the editor that published both the 1980 and 1981 articles in IER. I’m curious about what creative link you’ll make to bring us from bwcker 1973 to Manser and Browne and McElrou and Horne in 1980 and 1981

Let’s now introduce a Manser and Brown or McElroy and Horne. These two papers will be our focus. Firsr start off and introduce us to all four people. Who were they at the time? Who were their employers, what do we know about them ans this work?

Let’s start with Manser and Brown. Set up the paper for us. How do they motivate their papers reason for existence? What is the problem and how do they the problem up? Explain the link to Nash. What is the bash equilibrium in their model? And if they discuss power, what do they call it if they do, ans what is its source? Last what is the outside option or threat position? How does it shape the allocation of resources?

Write down the problem and agents utility functions. What are the endogenous choice variables? What is exogenous? What is the Nash equilibrium?

Do they allude to divorce at all? If so, what is its source? How does it relate to threat positions and surplus within the household?

Now let’s move into the McElroy and Horne. To the casual reader, these papers are the same so the goal here is to note the similarities but primarily their unique differences. Introduce the purpose of a second household model. Why was it needed?

Set up the model for us by showing the agents utility function and its argument. If the outside option exists, include it. Discuss each element and its role in the story of the model and then stop befoee going on.

Now let’s summarize the key elements of all three models and where the literature on marriage stood in 1981.

New section entitled the empirical household models. We want to note early work by Viner. I don’t know this literature so please summarize any if you know it. What if any was economists focus on marriage empirically in the 70s and 80s? I am leading us into the later work on divorce by Betsey Stevenson and Justin Wolfers as well as a paper by Lundberg and Pollack in the journal of Human Resources related to the idea of some testable predictions by the later bargaining model.

Okay rewrite this, but maybe mention empirical work that was akin to demography focusing on trends in marriage and divorce. Then note the empirical work done by the two papers but mention Lundberg and Pollack first. Here’s the gist. The Becker model has a unified budget constraint. If the wife has the income or the husband has the income, the allocations made are identical. But in the bargaining papers the link of total income to the spousal income was important. The if it was possible to find exogenous variation in one or the other, one could text elements of the model but the problem was, exogenous changes in a wife’s income would change total income and that did have effects in beckers model. What they needed was a change in spousal non-labor income that did not change total household income — a truly strange phenomena. But they found it in a natural experiment in England where the government changed innocuously the recipient of a household subsidy for poverty relief. It had gone first to husbands but then went to wives. This under Becker should have no change on demand as total income remained unchanged. But in the bargaining models the wife’s bargaining power had improved. They showed changes in the minds of goods purchase’s following the policy change. Despite total income being held constant, demand for female and specifically children goods rose but male consumption goods like alocohol ans tkbaxxo fell. SummariE this ysinf your knowledge of the paper and what I’ve said.

Okay we now want to focus on Betsey Stevenson and Justin Wolfers next because this is the second paper in my opinion that is very influential in the empirical literature on these models. Not only does the paper emphasize coasian reasoning, which has always been there in beckers work but which probably is easier to see in the bargaining papers because of the focus on outside options, it also linked it both to unilateral divorce laws, domestic violence, but also ironically early use of the difference in differences modeling with event studies. Write that as a sub section following the Lundberg and Pollack paper. By the way, I think I left off a third coauthor of theirs so we want to go back and clear that up before we rewrite the entire essay. Now discuss the coase theorem which basically states that the allocation of property rights don’t matter in exchange if transaction costs are small, but do if they are large. Unilateral divorce was unique not just from a historical perspective — it had once needed agreement to get a divorce — but it also had implications for property rights. Stevenson and Wolfers say that before unilateral divorce, the person wanting the marriage to stay together had all the power. But under unilateral divorce, the person wanting to exit had the power. Again, like Lundberg and coauthors, this seemingly small detail had in their minds ramifications not just for divorce but for domestic violence as well. The link to domestic violence is that one one reason but not the only reason or when the most common reason but nonetheless an important reason we allow people to exit divorces is in addition to Liberty people can become otherwise trapped in misery from loneliness to abuse itself. They looked at the effect then of the law changes ysinf diff in diff with event studies and focused on suicides and spousal homicides, and found female suicides fell as a result of the laws. Summarize all of this neatly. Make it flow, And emphasize that it’s lasting legacy was on many things like event studies, diff in diff, but bargaining theories of domestic violence as well as like Lundberg and coauthors finding beckers model wbile valuable lacked empirical content. And we see that the game theoretic models ironically did.

Conclude the essay. Here we note the development of the economic theory of marriage by noting that while Becker has been a major contributor, one could argue that it has been the game theorists who have had the biggest impact. The modern empirical work for instance tends to focus moreso on the bargaining itself and threat positions than was emphasized in Becker. But this essay leaves out a lot both empirically and theoretically. It leaves out the rich theoretical work of Shoshana Grossbard such as her early advances on polygamy and the numerous papers she has ushered into publication as editor of the review of economics of the household. It also leaves out the work of Pierre chiappori, who in many ways is descendent of both of these streams with his collective model that emphasizes Pareto efficiency. My selection is selective because in this essay, I have tried primarily to move into a branch of empirical work on domestic violence that focused on the outside option which is rooted in the work of early game theoretical models of the family from rhe 1980s. I also didnt discuss Lundberg and Pollack’s mid 90s paper on noncooperetivr bargaining called separate spheres.

Perfect. I think we have an essay. We now need to rewrite it. Since this goes in the direction of the domestic violence work, I think we want to start by saying that the empirical work on domestic violence by economists has many unique elements that to an outsider seem strange. Notably there is a focus on the outside option as a key factor in shaping whether and to what degree violence occurs in the family. So let’s now have a title based on this and an outline. Please maintain the structure of the material we’ve done already and give me a title, but note we are going to be focusing on what I just said before diving into this. I think I may note at the offset that new work on domestic violence appears all the time that has this flavor so it’s maybe helpful to give context.

Perfect. Okay. I want to open up the essay by noting a new paper by Emily nix at university of Southern California used Scandinavian linked registry data and was able to show that when a man and a woman matched, if she matched with someone who would later hit her, she showed the woman’s labor outcomes had fallen precipitously just after the cohabiting started. Their explanation was that the abusive man was eroding her outside options in order to keep her in an abusive partnership. In that paper are several elements that to the unread observer seem odd. Put aside it’s an economist studying marriage and abusive — something that itself alone will tend to draw curious looks. But there’s also the odd elements like outside options. Now explain that the purpose of this essay is to trace out the theoretical history of the marriage models through economists and game theorists to provide the reader with a theoretical understanding of where these ideas that are the focus of so many empirical work on violence in the family come from. Now write all this up in light of the direction the essay is going to go, but only for part 1.

Okay, now rewrite part 2 using the drafts we finally agreed on from earlier.

Remember we had agreed to expand this utility function to incorporate a broader household model with time. Please rewrite this entire section using the broader equation,

After you say “assumes harmonious household”, note that in subsequent work he did attempt to address the lack of harmony wit a “rotten kid theorem”, which focused not surprisingly on transfers to encourage cooperation. These methods are commonplace in this eras construction of modeling of the complex inner working of small societies where love and not prices allocated resources, and no doubt monetary transfers did move between members, but in time this was placed with a more generalized transferable utility conception. With this caveat, please rewrite the section, but still focus on the main theme that there was a unitsry utility function and a single family budget constraint, and outside options are not explicitly modeled.

Now summarize our old draft that goes with the new part 3 on bargaining in game theory.

Sorry repeat. Please take what we we have agreed hoping for part 3 and write it according to our new part 3 outline abt bargaining in game theory.

Are you sure this covered all the bullet points of the new section 3? Please rewrite it and be thorough. Include all we said and wrote before. But go into the introduction of bargaining theory, describe Nash, repeat the speculation abt the timing of it entering household work. I think this may be a good time to mention Pollack was editor of IER

Great. Now rewrite part 4 like we discussed using the finalized version thay incorporates all the edits we discussed

Now move into the next section writing what we discussed

Now reproduce the next section just like we discussed

Now go to the next section

Now conclude the essay

PleSe give this essay a title and a subtitle

Please rewrite a conclusion. Keep most of it but say that the idea of the threat position, rooted in these early bash bargaining models of marriage, are key parts of economisfs empirical contributions to the study of domestic violence. This essay was not exhaustive by any means but rather a simple sketch through the literature from game theory to empiricism. Say that we suspect this one part of the theory of the marriage has shaped a lot of the empirical work and will continue to as it’s been quite fruitful so far in helping understand domestic violence and the importance of outside options in deterring. But going forward, one thing I would like to see is more about the sorting into stable abusive relationships. Gale and Shapley had after all modeling the stable pairing in marriage as based on preferences and the deferred acceptance algorithm. Many men and women remain in abusive relationships, too, even with an outside option - a phenomena well documented in writings about “high conflict couples” which emphasizes the role of personality disorders in abuse. But these still do not adequately explain the stability elements and one future line of theoretical and empirical work might be to provide greater insight into why some abusive relationships are so stable even with available outside options. The “pull factors” as in the gravity keeping intact abusive relationships sometimes for years far beyond the initiation of abuse is not a topic economists have made contributions to, instead focusing almost entirely on abuse in the context of threat positions, but this is too myopic if no work emerges that focuses on the sorting into stable partnerships characterized by emotional, psychological and physical abuse. Why do they stay if they can leave in other words? What pulls them together? This would be a good route for future research. Please rewrite the conclusion incorporating the original conclusion with this new suggestion for future work

1. ChaptGPT mistakenly thought the citation came from his dissertation. I decided to leave the error.

2. Bringing up Rubinstein was a random idea I had while writing. Basically I just started to wonder about the simultaneous work on marriage by game theorists Gale and Shapley in early 60s and economist Gary Becker in early 70s. Then I was thinking about the bargaining models on marriage in the early 1980s and sort of remembered Rubinstein had been active on bargaining too. But his work isn’t really relevant to this; I just was wondering if ChatGPT might have ideas. But it never went anywhere. Decided to leave it.

3. I am curious about the employment that GPT-4 assigned to each of the four authors I review here. I asked GPT to mention employment but I don’t think it got them all four correct. Leaving it.

4. For both papers, I asked GPT “impute” what specifically each paper was about without much prompting. This was one of those cases where I couldn’t remember what precisely the papers unique contributions had been because in the 15 years since my dissertation, I had more or less merged them in my mind and simplified them so that I just remembered the threat position idea and the concept of bargaining over surplus as the main points. I think GPT4 also isn't getting everything right here as it gets redundant and in earlier iterations had said one of them hadn’t emphasized threat positions but in this final draft it treated them as more similar on that. Decided to leave it to show this is a case where I could’ve easily expanded on it in edits to fine tune the essay.